Described below is sensorless position determination for a magnetic bearing. Such a magnetic bearing is used for mounting an object, for example a rotor, with the aid of a magnetic field which is produced, in general, by at least one electromagnet.
The essential advantage of a magnetic bearing compared to a classical bearing, for example using a roller bearing, lies in its almost complete lack of friction. This represents an advantage, in particular in respect of its wear. On the other hand, it is only by this that a bearing mount for very rapidly rotating rotors becomes possible. One difficulty with electromagnetic bearing mountings is in the fact that electronic regulation of the position of the object which is to be mounted is indispensable. For this purpose, the main requirement is a determination of the position of the object relative to the electromagnet. In addition, the speed at which a change in position is completed can be determined directly. Classically, the position is determined directly using a position sensor. However, the use of a position sensor is associated with certain disadvantages. Of these, particular mention should be made of the fact that a position sensor throws up additional costs, a certain amount of installation space is required for building in the sensor, and the sensor can, if it fails, be responsible for a failure of the entire magnetic bearing system.
For this reason, in recent years a host of so-called sensorless or position-sensorless methods have been suggested for regulating a magnetic bearing. These methods forgo the use of a position sensor and attempt instead to draw conclusions about the position, and possibly also the speed, of the object for which the bearing is used, on the basis of the measurement of the electromagnet's current and the voltage. In these cases, the position sensor is replaced either by evaluation electronics or by an estimation and observation algorithm. This makes an estimate of the current position, and possibly also an estimate of the current speed, in each case relative to the object for which the bearing is to be used.
When one looks at known magnetic bearings, an electromagnet exercises an attractive force on a suspended body. Working against this attractive force are disruptive forces, e.g. the force due to the weight of suspended body. At a certain distance a balance of forces arises. At constant current the attractive force rises as the body approaches the electromagnet. It reduces if the body moves away from the electromagnet. Because of its physical characteristics, a magnetic bearing is unstable, and must therefore be controlled. Data about the movement behavior of the suspended body is obtained by a controller from a position sensor, for example. If the magnetic bearing is a sensorless one, an external sensing system is omitted. Since control/regulation is necessary even for sensorless magnetic bearings, the position data required for the purpose is obtained by the characteristics of the electromagnet which depend on the air gap.
The basic principle of sensorless position determination for a magnetic bearing, using measurement of the voltage and current, can be seen by reference to FIG. 1. FIG. 1 shows a sketch of the principle of a magnetic bearing 10. Seen here is a unidirectional bearing with an electromagnet 200. Together with the object 100 for which the bearing is required, a pole 210 of the electromagnet 200 forms an air gap 20, the size 1 of which changes as a function of the position r of the object 100. The formula used for calculating the magnetic resistance Rm of the air gap 20 is
                              R          m                =                  1                                    μ              o                        ⁢            A                                              (        1        )            where the length l=l0−r, the nominal length l0 together with the effective area A of the air gap and the permeability μ0 of air.
If one neglects from here on the magnetic resistance of the iron core of the electromagnet 200 and that of the object 100, then the inductance L of the magnetic bearing 10 is calculated in the form of the equation
                              L          ⁡                      (            r            )                          =                                            M              2                                      R              m                                =                                                    M                2                            ⁢                              μ                0                            ⁢              A                                                      1                0                            -              r                                                          (        2        )            where M is the number of windings in the electromagnet 200. It is clear that the inductance of the system is an inversely proportional function of the distance of the object 100 from the poles of the electromagnet 200. This essential characteristic represents the basis for many estimation and observation algorithms for determining the position of the object 100. In this connection, the following publications from the related art should be noted: D. Pawelczak, “Nutzung inharenter Messeffekte von Aktoren and Methoden zur sensorlosen Positionsmessung im Betrieb” [The use of inherent measurement effects of actuators and methods for the sensorless measurement of position in operation], Diss., Universitat der Bundeswehr Munchen, 2005; N. Skricka, “Entwicklung eines sensorlosen aktiven Magnetlagers” [Development of a sensorless active magnetic bearing], Fortschritt-Berichte, Vol. 8, No. 1027, VDI-Verlag Düsseldorf, 2004; and Yuan Qing Hui et al., “Self-sensing actuators in electrohydraulic valves”, Proceeding of the International Mechanical Engineering Congress and Exposition, Anaheim, Calif., 2004.
A host of aids exist for the sensorless operation of a magnetic suspension system, the essential approaches of which, together with their advantages and disadvantages, are itemized and analyzed in DE 10 2008 064 380 A1. In that are discussed observer-based methods, parameter estimation methods and various groups of methods for the determination of inductance. The latter methods exploit the fact that the inductance of a magnetic bearing depends on the position of the object. Thus a measurement of the inductance permits the position of the object to be determined.
DE 10 2008 064 380 A1 itself, on which the present application builds, finally proposes a method for the sensorless estimation of the state of magnetic suspension systems in which the position is determined by an evaluation of the current and the voltage. However, in the method there described, an inaccuracy can arise because the electrical resistance of the magnetic bearing, which must be an input when determining the inductance, is not adequately taken into account.